Next, we apply this analysis to the translation generators. \(P_{-\frac{1}{2}, -\frac{1}{2}}\)  was used in [1]} to show that the coefficients of the primary must obey
\( C_{p}^{(0)}({\bar{h}}_1+\tfrac{1}{2}, {\bar{h}}_2)+C_{p}^{(0)}({\bar{h}}_1, {\bar{h}}_2+\tfrac{1}{2})= C_{p}^{(0)}({\bar{h}}_1, {\bar{h}}_2).\) 
